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An interference channel is said to have strong interference if a certain pair of mutual information inequalities are satisfied for all input distributions. These inequalities assure that the capacity of the interference channel with strong interference is achieved by jointly decoding the signal and the interference. This definition of strong interference applies to discrete memoryless, scalar and vector Gaussian interference channels. However, there exist vector Gaussian interference channels that may not satisfy the strong interference condition but for which the capacity can still be achieved by jointly decoding the signal and the interference. This kind of interference is called generally strong interference. Sufficient conditions for a vector Gaussian interference channel to have generally strong interference are derived. The sum-rate capacity and the boundary points of the capacity region are also determined.